Wheel bearing apparatus exist for driving wheels and driven wheels to support a wheel of a vehicle that rotatably supports a wheel hub that mounts a wheel via a rolling bearing. For structural reasons, the inner ring rotation type is used for driving wheels and both the inner ring rotation type and the outer ring rotation type are used for driven wheels. Double row angular contact ball bearings, with low rotational torque characteristics, are popularly adopted in the wheel bearing apparatus. These bearings have a desirable bearing rigidity, exhibit high durability against misalignment and improve fuel consumption. In the double row angular contact ball bearing, a plurality of balls is interposed between a secured ring and a rotational ring. The rings contact the balls by applying a predetermined contact angle to the balls.
The wheel bearing apparatuses are broadly classified into the first, second, third and fourth generation type. In the first generation type, a wheel bearing includes a double row angular contact ball bearing fit between a knuckle, forming part of a suspension apparatus, and a wheel hub. The second generation type has a body mounting flange or a wheel mounting flange directly formed on the outer circumference of an outer member (outer ring). The third generation type has one inner raceway surface directly formed on the outer circumference of a wheel hub. The fourth generation type has the inner raceway surface directly formed on the outer circumferences, respectively, of the wheel hub and the outer joint member of the constant velocity universal joint.
In recent years, there have been strong desires to improve “NVH” i.e. “Noise”, “Vibration” and “Harshness” to say nothing of improving the durability and reducing the manufacturing cost. As shown in FIG. 11, a prior art wheel bearing 50 used in the wheel bearing apparatus is formed by a double row angular contact ball bearing. It includes an outer member 51 formed on its inner circumference with a double row outer raceway surface 51a with a circular arc cross-section. A pair of inner rings 52, 52 each includes an inner raceway surface 52a on its outer circumference. The inner raceway surfaces 52a have a circular arc cross-section and they oppose the double row outer raceway surfaces 51a. Double row balls 53 are contained between the outer and inner raceway surfaces, via a cage 57. The bearing portion of each row has a contact angle α. A seal 54 is mounted in annular openings formed between the outer member 51 and the inner ring 52 to prevent leakage of lubricating grease sealed within the bearing and the entry of rain water or dust into the bearing from the outside.
As shown in FIG. 12, the higher shoulder edges 55, 56, in cross-section, of the outer and inner raceway surfaces 51a, 52a, are formed with auxiliary raceway surfaces 55a, 56a smoothly continuous, respectively, to curves “a”, “b” of the circular arc cross-section. Each of the auxiliary raceway surfaces 55a, 56a has a cross-section formed by a curve or straight line having a curvature smaller than that of the curves “a”, “b”. Chamfered portions 55b, 56b each have a circular arc cross-section and are continuous with the auxiliary raceway surfaces 55a, 56a. 
In such a wheel bearing apparatus, with the auxiliary raceway surfaces 55a , 56a, when a large load amount is loaded on the bearing and the contact angle α increases, the contact ellipse of ball 53 is “pushed out” from each raceway surface 51a , 52a to the auxiliary raceway surfaces 55a, 56a. However, since the auxiliary raceway surfaces 55a, 56a are smoothly continuous with the curves “a”, “b”, forming the cross-section of the raceway surfaces 51a, 52a, and have straight cross-sections, the generation of the edge load (excessive stress) will be prevented. However, the contact ellipse is pushed out to the auxiliary raceway surfaces 55a, 56a. 
In addition, each of the auxiliary raceway surfaces 55a, 56a has a straight cross-section. Thus, it is possible to set the inclination of the auxiliary raceway surfaces 55a, 56a larger as compared with an inclination formed by an extension of the circular arc curves “a”, “b” of the raceway surfaces 51a, 52a. Also, the inner diameter of the outer member 51 is set to be small or the outer diameter of the inner ring 52 is set to be large. Accordingly, a condition where the auxiliary raceway surfaces 55a, 56a have to be ground using a side surface of a grinding wheel can be avoided. Thus, grinding time can be reduced.
In addition, the raceway surfaces 51a , 52a have, respectively, the chamfered surfaces 55b, 56b with circular arc cross-section, continuous to edges of the auxiliary raceway surfaces 55a, 56a . Thus, the edge load of the contact ellipse can be further reduced (see Japanese Laid-open Patent Publication No. 2007-85555).
In this kind of wheel bearing apparatus, the contact ellipse of the ball 53 overrides the shoulder portion of the raceway surface if an excessive load is input onto the wheel bearing from a wheel. Thus, indentations are generated on the shoulder and cause abnormal noise when a vehicle climbs a curb. In order to solve the indentation problem caused in the shoulder of the raceway surface, it is necessary to increase the shoulder height of the raceway surface. However, an increase in the shoulder height causes problems like an increase in the weight of wheel bearing, reduction of its workability and finally an increase in manufacturing costs. On the other hand, sufficient sealability will not be assured due to a reduction of the cross-section height of the seal 54 and an increase in height of the shoulder of the inner ring 52, if it is increased. In the present specification, the term “shoulder overriding” means a phenomenon where the contact ellipse formed in a contact portion between the ball 53 and the outer raceway surface 51a is pushed out from the corner between the inner diameter of the outer member 51 and the outer raceway surface 51a . This generates the edge load when a large moment load is applied to the wheel bearing.